bioware is so misleading, they make a character trailer for a chick who dies an hour into the game. unlike other temporary companions in origins, she actually can get experience and approval/disapproval
Well if they didn't then no one would be surprised when she died. I don't think there is any way that Mhairi could survive the Joining. Whether they can survive or not depends on the strength of their immune systems and ability to withstand the taint. It's speculatd when Oghren can still talk after Joining that being a heavy drinker could help since your body already processes lots of toxins.
Unless they were going to be really cheap, your actions should not affect whether Mhairi can handle the taint. She likes you a little, dislikes you a little, or is neutral? In Origins you can hate Duncan for conscripting you, love him for saving you and/or getting you out of the hellhole you started in, or not really care one way or another and you still live. Oghren and/or Anders also become Wardens? True she doesn't like them, but chances are you don't like either Daveth or Ser Jory - or both - and you survive just fine.
I don't really get all this Mhairi love anyway. All she does is swear vengeance on the guy who killed Roland or whoever he was and disapprove of Oghren and Anders. She might have been okay with allowing Sigrun into the Wardens, but she would have freaked out about Justice and Velanna, too. She was really far too uptight and by-the-book to really be a Warden.